A Conditional-Value-at-Risk Framework for Multi-Stakeholder Optimization

We use CVaR to create a general framework for computing compromise solutions in a multi-objective, multi-stakeholder setting. In this setting, we sample the preferences of a population of stakeholders and we observe that the stakeholder dissatisfactions (distance to their utopia points) can be interpreted as random variables. Consequently, we shape the dissatisfaction distribution by solving a CVaR minimization problem parameterized in the probability level. We use the concept of the CVaR norm to give a geometric interpretation to this problem and note that the CVaR formulation includes average and worst-case approaches previously proposed in the literature. We also use the properties of the CVaR norm to prove that the CVaR minimization problem yields Pareto optimal solutions for any choice of the probability level. We discuss the use of the generalized entropy index to compute compromise decisions with fairness guarantees. This is joint work with Alex Dowling and Luis Fabian Fuentes.